Any way to make the mirrored mesh more idiomatic?
No, there is currently no way to do this. You only select the vertices that you see on the geometry generated with the Mirror modifier, but what you transform are the original vertices. 

You could temporarily mirror the whole object by multiplying its scale by -1 on the mirroring axis so the original geometry is on your preferred side. You can just enter -1 after pressing s followed by the axis, in this case x in object mode, or you could also use the dedicated Mirror operator(Ctrl+m) to do this, or just enter *-1 in the numeric input field in the n panel, Transform tab, under Scale or in the Properties Editor's Object tab.